sectheta= 1costheta = 1sintheta = costhetasintheta Each denominator must be nonzero. Cotangent equals 1/tan θ only where both expressions exist. For P(x,y)!= O, let r=sqrt(x2+y2)>0. **Ratio** | **Coordinate form** sintheta | y/r costheta | x/r tantheta | y/x, x 0 cosectheta | r/y, y 0 sectheta | r/x, x 0 cottheta | x/y, y 0 Powers and inverse functions cosntheta=(costheta)n, and similarly for sine and tangent, for positive integers n. cos-1x denotes the inverse function, not 1/cos x. The same convention applies to sine and tangent. y=cos-1x y=x and 0 <= y <= pi, for -1 <= x 1. y=sin-1x y=x and -(pi)/(2) <= y <= (pi)/(2), for -1 <= x 1. y=tan-1x y=x and -(pi)/(2)<y<(pi)/(2), for real x.

\(\sec\theta=\dfrac1{\cos\theta}\qquad\operatorname{cosec}\theta=\dfrac1{\sin\theta}\qquad\cot\theta=\dfrac{\cos\theta}{\sin\theta}\)

Each denominator must be nonzero. Cotangent equals 1/tan θ only where both expressions exist.

For \(P(x,y)\ne O\), let \(r=\sqrt{x^2+y^2}>0\).

\(\cos^n\theta=(\cos\theta)^n\), and similarly for sine and tangent, for positive integers \(n\).

\(\cos^{-1}x\) denotes the inverse function, not \(1/\cos x\). The same convention applies to sine and tangent.

\(y=\cos^{-1}x\iff\cos y=x\text{ and }0\leq y\leq\pi\), for \(-1\leq x\leq1\).

\(y=\sin^{-1}x\iff\sin y=x\text{ and }-\frac{\pi}{2}\leq y\leq\frac{\pi}{2}\), for \(-1\leq x\leq1\).

\(y=\tan^{-1}x\iff\tan y=x\text{ and }-\frac{\pi}{2}<y<\frac{\pi}{2}\), for real \(x\).

The six trigonometric ratios

The six trigonometric ratios

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